Nuclear density functional theory (NDFT) has proven a powerful tool in our quest to understand the complexities of nuclear structure. Whilst it naively may appear preferable to derive a theory of nuclear structure from the underlying strong force, this is difficult-to-impossible for all but very light nuclei as QCD is asymptotically free. NDFT, however, describes nuclear systems using an energy functional of particle density currents, and has universal application across the nuclear landscape. Unfortunately, such functionals typically have little direct connection to the underlying strong physics. Furthermore, they are typically phenomenological by necessity and require a large array of free parameters to be fitted to experimental data. This limits both physical understanding and predictive power.
In this talk, I demonstrate that effective field theory (EFT) is a potential method of ameliorating both problems. I apply EFT to quantum field theories involving the exchange of two to four types of mesons, and show that the resulting fitted functionals show comparable performance to standard Skyrme-type functionals with respect to usual quantities such as the binding energies and charge radii of nuclei. This is achieved whilst only having to fit a fraction of the number of free parameters as standard Skyrme-type functionals. In doing so I suggest that some of the hitherto-free parameters in Skyrme-type functionals may be mathematically related or constrained, in particular the poorly-understood isovector contribution to the nuclear spin-orbit interaction.
I anticipate that this approach may open a new method of constraining functionals commonly used in the study of nuclear structure by potentially reducing the number of parameters that require fitting. Furthermore, this work suggests that EFT may serve as a “bridge" between high-energy models of nuclear force that are theoretically sound, but have limited applicability, and more universal, but more phenomenological, approaches such as NDFT.